Take the real-life situation and create an equation or inequality that could be used for analysis, prediction, or decision making. Then, draw a graph to depict the variables in your situation. Use your graph and what you know about linear inequalities to discuss the significance of your findings.

My answer:

In 2005, the amount of registered births in NYC was 560. Each year, the number of births increases by 420. When will this amount increase to 5000?

How would I put this into a linear equation and graph. Any help would be appreciated.

Please check your figures. I can't believe that only 560 births were registered in NYC in 2005. It also doesn't make sense that they almost double each year(420).

you said
births = 420*years + 560

wow, looks like you just formed your linear equation.

for your second question, when will there be 5000 birtsh?

5000 = 420*years + 560

I am pretty sure you can solve this for "years", your answer will be the number of years since 2005 of course.

Could I graph that?

sure you could.
As Ms. Sue said, your data does not make a lot of sense, but nevertheless you can graph it.
let t=0years, births =560 ---> (0,560)
let t=5 years, births=2660 --> (5,2660)

you got 2 points, it is a straight line, so.....

You can plot these two points on a graph and draw a straight line through them. The x-axis represents the number of years since 2005 and the y-axis represents the number of births.

Now, let's analyze the significance of this graph and the linear inequality.

In this case, the linear equation represents the relationship between the number of years since 2005 and the number of births. It assumes a constant rate of growth, where each year the number of births increases by 420.

By setting the equation equal to 5000, you are asking at what point in time the number of births will reach 5000. Solving the equation for "years" will give you the answer.

When you graph this linear equation, you can see the trend of increasing births over time. The line will have a positive slope, indicating that as the number of years increases, the number of births also increases.

The significance of this graph is that it allows you to visually analyze and understand the trend. By looking at the graph, you can estimate when the number of births will reach 5000. If the line intersects the y-axis at (0,560), it implies that in the year 2005, there were 560 births. As the line slopes upwards, it shows that the number of births is increasing year after year.

Using linear inequalities, you can make predictions about future birth rates based on the established trend. If you wanted to know when the number of births would exceed a certain value, you can set up a new inequality and solve for "years". This allows you to make informed decisions or predictions based on the data.

However, it's important to note that this analysis is based on the assumption of a constant growth rate, which may not reflect real-life scenarios accurately. Due diligence is required when making decisions or predictions based on linear equations and inequalities.